crooked cubes

the eight vertices (corners) of a cube wander around their assigned position, changing the square faces into trapezoids and rectangles. the official unit cube (pink) sits there, unperturbed, while the crazy crooked (green) cube intersects with it, and other surprises ensue. can you figure out whether the volume of the crooked cube is changing?

cuboctahedron with worms

a cuboctahedron has two squares and two triangles meeting at each vertex. so it has four edges at each corner ball, allowing for an eulerian circuit, a path that traces all edges exactly once. these three colored worms chase each other around the play structure, forever!

exploding parabola

the classic case of red vs blue... but this overlooks all the other colors that can spring up! rainbow beads follow trigonometric paths in space, drawn in mathematica.

squirming dodecahedron

what happens if you let the vertices of a polyhedron wander around in circles? the edges have to strain to stay connected, and the faces may not all be planar, but don't judge. there are 12 "faces" and 20 wiggling green vertices. can you find how many edges there are, without counting?